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Thermodynamics and mechanical laws of causal-diamond horizons

Carlos R. Ordóñez1 and Gustavo Valdivia-Mera1,2,*

  • *Contact author: gvaldiviamera@uh.edu

Phys. Rev. D 114, 085028 – Published 30 October, 2026

DOI: https://doi.org/10.1103/mqsp-mwbs

Abstract

We develop a unified thermodynamic and mechanical framework for causal-diamond horizons in Minkowski spacetime. Euclidean regularity fixes the temperature TD=1/(πα), where 2α is the temporal extent of the diamond. The regulated Gibbons-Hawking-York contribution gives IDE=−A0/(4G), with A0 the area of the horizon bifurcation surface, and the vanishing equilibrium geometric energy then yields the entropy-area relation SD=A0/(4G). For weak matter perturbations crossing a localized portion of the future horizon, a Raychaudhuri analysis relates the associated Killing-energy flux to the area response, yielding a local physical-process first law at leading order near the bifurcation surface and, for classical matter satisfying the null energy condition, a local second law. Uniform conformal surface gravity establishes the zeroth law, while zero temperature is approached only in the limit α→∞, in which the finite causal horizon disappears. These results show that a coherent horizon-law structure can arise within a causal diamond, a fundamental building block of the causal structure of Minkowski spacetime. The derivation is explicit in (2+1) dimensions, while the physical results retain the same form for spherical causal diamonds in d≥3.

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